Explore the 9/11 series

Speaking to the crowd at Ground Zero, the president quoted the Bible: "Therefore, we will not fear, even though the earth be removed, and though the mountains be carried into the midst of the sea."

New York Mayor Michael Bloomberg said a "perfect blue sky morning" had turned into "the blackest of nights" on 9/11.

"They were our neighbours, our friends, our husbands, wives, brothers, sisters, children and parents," he said of the victims.

"They each had a face, a story, a life cut short from under them."

Analysis

By Mark MardellBBC North America editor

These ceremonies around America are no perfunctory moments of remembrance of an event that has faded in the popular imagination. These day-long events are designed to recall the horror and loss of that day, to play on the heart strings of a nation that cannot forget.

Around New York and Washington there is a very obvious reminder of the way the country has changed, a police presence that must be unprecedented, closing down lower Manhattan to traffic for a day - the reaction to what authorities say is a very real threat from al-Qaeda.

The American homeland has not been attacked again since 9/11, the sense of possibility, of vulnerability, the overwhelming need for security has not gone away. But some things have changed.

Today may have evoked memories of a righteous patriotic fervour to deal with those who threaten the country and that desire does still exist but the enthusiasm to reshape the destiny of other countries to make Americans safer has largely disappeared.

All of the victims' names were read out amid tears, the five-hour reading punctuated by the solemn silences, and music.

Bagpipers opened the gathering, the Brooklyn Youth Chorus sang the national anthem, the cellist Yo-Yo Ma performed, and Paul Simon played his classic song The Sounds Of Silence.

Mourners streamed into the newly opened memorial, which has two reflecting pools, each almost an acre in size, in the footprints of the twin towers.

They placed pictures and flowers beside names etched in bronze. Grown men and women sobbed in grief over the inscriptions.

Behind the memorial could be seen the gleaming bulk of One World Trade Center, now three-quarters completed.

Mr Obama and his wife, Michelle, attended ceremonies in New York, Pennsylvania and at the Pentagon.

At Ground Zero he joined his predecessor, George W Bush, to visit the memorial. With bowed heads, they touched inscriptions.

From New York, the Obamas travelled to the field on Shanksville, Pennsylvania, where the fourth plane was forced down by passengers who fought back.

The couple laid a wreath of white flowers at a new marble memorial to the 40 passengers and crew of the lost plane, before moving on to the Pentagon, outside Washington DC, where another wreath was laid.

In New York, metal barriers were erected on roads near Ground Zero, while police in New York and Washington are stopping and searching large vehicles entering bridges and tunnels.

The CIA received a warning last week that al-Qaeda might have sent attackers, some of them possibly US citizens, to bomb one of the cities.

The warning was described by officials as "credible but unconfirmed".

'New generation of patriots'

In an earlier speech at the Pentagon, Vice-President Joe Biden praised the US soldiers who had killed al-Qaeda leader Osama Bin Laden in Pakistan in May of this year.

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A "new generation of patriots" were galvanised by 9/11, he told a military audience.

"We will not stop - you will not stop - until al-Qaeda is disrupted, dismantled and, ultimately, defeated."

Sunday's ceremonies began at the US embassy in the Afghan capital, Kabul, where the flag was lowered to half-mast to remember those who died 10 years ago, as well as those who have died since. A piece of the twin towers is buried underneath the flag pole.

US forces were sent to Afghanistan to oust the Taliban from power after they had given sanctuary to al-Qaeda.

Overnight, insurgents attacked US bases in Bagram and Wardak, injuring about 80 US troops and killing two Afghan civilians, officials say.

More than 6,200 members of the US military have been killed in the wars in Iraq and Afghanistan.